Chapter 6: Q 6.95 (page 619)

Solve $18 a^{2} - 30 = - 33 a$

Short Answer

Expert verified

The value is $a = \frac{2}{3}, \frac{- 5}{2}$

Step by step solution

Given information

Given the equation, $18 a^{2} - 30 = - 33 a$

Writing in standard form

Writing in standard form, we get

$18 a^{2} - 30 = - 33 a 18 a^{2} + 33 a - 30 = 0 3 (6 a^{2} + 11 a - 10) = 0$

Using zero factor principle

Using the principle, we get

$6 a^{2} + 11 a - 10 = 0 6 a^{2} + 15 a - 4 a - 10 = 0 3 a (2 a + 5) - 2 (2 a + 5) = 0 (3 a - 2) (2 a + 5) = 0 a = \frac{2}{3}, - \frac{5}{2}$

Checking the value

Substituting and checking the value, we get

$18 {(\frac{2}{3})}^{2} - 30 = - 33 (\frac{2}{3}) 18 \times \frac{4}{9} - 30 = - 22 8 - 30 = - 22 - 22 = - 22$

This is true

Checking for another value

Checking, we get

$18 {(\frac{- 5}{2})}^{2} - 30 = - 33 (\frac{- 5}{2}) 18 \times \frac{25}{4} - 30 = \frac{165}{2} \frac{165}{2} = \frac{165}{2}$

This is true

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Solve $18 a^{2} - 30 = - 33 a$

Short Answer

Step by step solution

Given information

Writing in standard form

Using zero factor principle

Checking the value

Checking for another value

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Solve18a2-30=-33a

Short Answer

Step by step solution

Given information

Writing in standard form

Using zero factor principle

Checking the value

Checking for another value

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Logic and Functions

Probability and Statistics

Mechanics Maths

Calculus

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Solve $18 a^{2} - 30 = - 33 a$